The present invention relates to apparatus and methods for measuring heat transfer distributions on a surface and obtaining surface heat transfer data for a variety of cooling jet impingement configurations on the surface at different Reynolds numbers and particularly relates to apparatus and methods for determining local heat transfer distribution and Nusselt numbers for the heat transfer coefficients.
In many industrial applications, it is important to have detailed information concerning the heat transfer characteristics of a surface, especially in product design, as they enable a design engineer to better predict and understand thermal gradients, non-uniformity and other characteristics of heat transfer distribution which current methods cannot provide. For example, in industrial applications such as a gas turbine, a surface cooled by impingement of air jets can result in non-uniform surface temperatures and high temperature gradients. The temperature gradients, however, cannot be ascertained without knowing the temperature distribution of the surface of interest. Average surface temperatures fail to describe the temperature gradients or the non-uniformity of heat transfer that may exist. Both can be detrimental to a design. For example, a design which meets average temperature requirements may fail due to thermal fatigue if the temperature gradients are high.
In one approach, thermocouples have been mounted to a surface being cooled and used to measure temperature. However, there temperature measurements are a function of the locations of the thermocouples. If the thermocouple is positioned beneath an impinging jet of cooling air, it will read a higher temperature than if located between jets of impinging cooling air. Thus, the thermocouple may not accurately reflect the temperature of the surface. The thermocouple reading is often reported as a mean temperature, which is not correct because the thermocouple only averages temperature locally rather than along the entire surface.
In one prior report, a transient liquid crystal technique was used to measure heat transfer under an array of orthogonal jets. A thin coating of liquid crystal was sprayed on the impingement surface. The jet Reynolds numbers tested were between 4,800 and 18,300, the latter Reynolds number being a fairly low number. Moreover, the technique employed was transient rather than steady state. Additionally, the liquid crystal spray can be unreliable if not applied correctly. In any event, such research was limited to orthogonal impinging jets. See Huang, Y., Ekkad, S., and Han, J., xe2x80x9cDetailed Heat Transfer Distribution Under an Array of Orthogonal Impinging Jets,xe2x80x9d Journal of Thermophysics and Heat Transfer, Vol. 12, No. 1, January-March 1998.
Another technique measured the effect of a jet angle from a single jet of hot air impinging on a water cooled impingement plate. A calorimeter measured the rise in temperature of a metered flow of water from which the heat flow was determined and ultimately the heat transfer distribution on the plate was derived. This data, however, is derived using only a single jet of hot air whereas arrays of jets are more common in practice. Accordingly, there is a need for an apparatus and methods for quantitatively describing local heat transfer effects.
In accordance with a preferred embodiment of the present invention, there is provided an apparatus and method for determining local heat transfer distribution for a surface being cooled using an array of impinging jets, both orthogonal and angled relative to the surface, employing a broadband liquid crystal as a temperature sensor, air as a cooling medium, and a thin foil heater to provide constant heat flux for measuring both smooth and roughened surfaces over a range of jet Reynolds numbers between 10,000 and 35,000. The apparatus is also capable of achieving higher ranges of jet Reynolds numbers.
The apparatus employs a pressure chamber for flowing air under pressure through orifices of a jet plate at constant angles to provide either orthogonal or angled impingement air jets onto a smooth or rough surface. The surface is preferably heated using a thin foil heater adhered directly to the bottom of the test plate surface to provide a constant heat flux boundary condition. A calibrated liquid crystal sheet is mounted on the side of the heater element remote from the surface. Preferably, an insulating cover is placed on the liquid crystal face to reduce heat losses while enabling visual observation of the temperature, i.e., color fields, of the impingement surface. The plenum, jet plate, test plate, heater, liquid crystal and insulating material are placed in a pressure vessel, and enabling control of the pressure ratio across the plate, enabling the tests to be run at higher jet Reynolds numbers than possible if air was discharged directly into atmosphere. A camera is used to capture the images through a window of the pressure vessel and insulating material.
With the supply of air in the pressure vessel controlled to a particular temperature and pressure, liquid crystal temperature profiles are digitally recorded by computer and an image analysis system converts the liquid crystal image data into temperature distributions. A calibration curve is first generated by applying a temperature gradient between opposite ends of a liquid crystal strip and obtaining temperature measurements at equal distances along the strip. The calibration curve is digitized. Using the digitized calibration curve, a text file containing temperature at each pixel in the image captured is created. The text file contains a two-dimensional array of data, the intersection of each row and column representing a single pixel. This text file is then transformed into heat transfer coefficients and Nusselt numbers. Because the liquid crystal operates over a broad band of temperature, e.g., 5xc2x0 or less, and since surface temperature variations are greater than the bandwidth of the liquid crystal, several images are taken at various heat flux levels to provide a color change in each element of the liquid crystal. The images are superimposed and averaged to yield the heat transfer distribution on the entire surfacexe2x80x94assuming that the heat transfer coefficients are not a function of heat flux.
To determine the heat transfer coefficient distribution, the partial distributions of the individual images are averaged. Thus, the heat transfer coefficient distribution for a first image and all subsequent images are recorded. The average heat transfer coefficient at each pixel for all images taken is likewise recorded. Once the overall heat transfer coefficient is obtained, the overall Nusselt number distribution for the surface based on this overall average heat transfer coefficient is determined. These steps may be repeated for each plate configuration at each Reynolds number, i.e., for plate configurations having jet impingement angles of 90xc2x0, 60xc2x0, 30xc2x0 or the like.
In one aspect, the present invention provides a method of measuring local heat transfer characteristics of an object surface, the method comprising the steps of flowing a cooling medium onto the surface; sensing the temperature of the surface by juxtaposing a liquid crystal element and the surface; measuring temperature distributions of each pixel of the liquid crystal element at various heat flux levels; processing the temperature distributions to obtain temperature distribution profiles at each heat flux level; determining heat transfer coefficients of each pixel at each heat flux level; and determining an average heat transfer coefficient profile at each pixel. The method further includes determining an overall Nusselt number from the average heat transfer coefficient profile, calibrating the liquid crystal element prior to the processing step to determine temperature distribution profiles. The method further includes saving the temperature distribution profiles and filtering the heat transfer coefficients at each pixel to remove artificially negative data points.
In another aspect, in an apparatus comprising a heater element and a liquid crystal element juxtaposed in temperature sensing relation to an object surface, a method of measuring local heat transfer distribution along the surface comprising the steps of: obtaining steady state images of the liquid crystal element as a function of the sensed temperature of the surface at various heat flux levels; processing the steady state images to determine temperature distribution profiles at each pixel along the liquid crystal element; determining heat transfer coefficients for each temperature distribution profile; and determining an average heat transfer coefficient profile.
In a further aspect, a method for measuring local heat transfer distribution of an object surface, the method comprising the steps of: directing cooling air onto the surface; providing a liquid crystal element on a side of a heater element remote from the surface; energizing said heater element to various heat flux levels; measuring temperature distributions of various pixels of the liquid crystal element at the various heat flux levels; processing said temperature distributions to obtain temperature distribution profiles; and obtaining heat transfer coefficients for each distribution profile.
In yet another aspect, an apparatus for measuring local heat transfer distribution of an object surface, comprising a heater element for providing heat flux; a test plate disposed on a surface of the heater element for receiving impinging cooling air; a liquid crystal element on a side of the heater element remote from the surface; an insulating material disposed adjacent to the liquid crystal element and remote from the heater element; and means for determining heat transfer distribution coefficients from said liquid crystal element. The heater element preferably is a thin foil heater. The insulating element may be formed of a transparent material. The apparatus further includes a liquid crystal video thermographic system for capturing images of the liquid crystal element at various heat flux levels, and a computer system for controlling and monitoring various elements of the apparatus. The computer system preferably includes a memory device to store images of the liquid crystal element.
In yet another aspect, an apparatus for measuring local heat transfer distribution of an object surface, comprising: a liquid crystal element; a heater element for heating the liquid crystal element to various heat flux levels; the liquid crystal element disposed adjacent to the heater element for measuring heat transfer distributions of the object surface; means for capturing images of the liquid crystal element at each heat flux level; and means for determining heat transfer coefficients from the captured images.
In another aspect, an apparatus for measuring local heat transfer characteristics of an object surface, comprising: means for flowing a cooling medium onto the surface; means for sensing the temperature of the surface by juxtaposing a liquid crystal element and the surface; means for measuring temperature distributions of each pixel of the liquid crystal element at various heat flux levels; means for processing the temperature distributions to obtain temperature distribution profiles at each heat flux level; means for determining heat transfer coefficients of each pixel at each heat flux level; and means for determining an average heat transfer coefficient profile at each pixel. The apparatus further includes means for determining Nusselt numbers from the average heat transfer coefficient profiles.